It is heavily dependent on the individual. My first dog we had growing up, we just had to keep her bowl full and she ate when she was hungry. After she died and we got our next dog, we started out doing the same thing, and he ballooned up into a total fatty.
My boyfriend's first dog was able to be free fed and never overate. When he got a puppy, it would eat whatever it could find and ballooned up. The vet said if he just kept refilling the bowl, the dog would adapt to the fact that it would get enough to eat and learn to pace herself. Nope! She would eat, go vomit, then come back to eat more. Her brain is just wired different, so she's on a very strict diet.
Depends on the cat. Some are grazers that will just eat a little here and there and others will eat everything in the bowl so fast the throw it up. So some of it is just luck.
When i adopted my cat, she was OBESE. BIG TIME. I put her on a diet, and now she's normal sized, but she has a belly flap that won't go away. So it can happen.